answer with explanation

(a) Write down the probability distribution for the random variable, X, whose probability generating function is Gx(2) = 3 -2z. Show details of your workings. (7 marks) ( b ) If random variable Y is such that Y = aX + b, analyse and express the probability generating function of Y, Gy(z) , in terms of the probability generating function of X, Gx(z) . Show your workings in detail. (6 marks)